Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 360, pp. 122 - 130

We study the mean-square stabilizability of Itô stochastic systems with delayed input. In contrast to most previous results, where only sufficient condition...

Receding horizon control | Itô systems | Lyapunov type inequality | Delayed input | Stabilization | School construction

Receding horizon control | Itô systems | Lyapunov type inequality | Delayed input | Stabilization | School construction

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 16

We prove an inequality for the pth power of the norm of a stochastic convolution integral in a Hilbert space. The inequality is stronger than analogous...

60H10 | 60G51 | Mathematics | stochastic convolution integral | Lévy noise | Itô-type inequality | monotone operator | Analysis | Mathematics, general | Applications of Mathematics | 47H05 | 60H15 | stochastic evolution equation | 47J35 | MATHEMATICS | Levy noise | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | STOPPED DOOB INEQUALITY | Ito-type inequality | MONOTONE NONLINEARITY | Norms | Convolution integrals | Hilbert space | Stochasticity | Inequalities

60H10 | 60G51 | Mathematics | stochastic convolution integral | Lévy noise | Itô-type inequality | monotone operator | Analysis | Mathematics, general | Applications of Mathematics | 47H05 | 60H15 | stochastic evolution equation | 47J35 | MATHEMATICS | Levy noise | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | STOPPED DOOB INEQUALITY | Ito-type inequality | MONOTONE NONLINEARITY | Norms | Convolution integrals | Hilbert space | Stochasticity | Inequalities

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 248, Issue 5, pp. 1230 - 1255

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone...

Demicontinuous | Burkholder inequality | Asymptotic stability | Mild solution | Itô-type inequality | Semi-monotone | MATHEMATICS | EXPONENTIAL STABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | Ito-type inequality | UNIQUENESS

Demicontinuous | Burkholder inequality | Asymptotic stability | Mild solution | Itô-type inequality | Semi-monotone | MATHEMATICS | EXPONENTIAL STABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | Ito-type inequality | UNIQUENESS

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 10/2017, Volume 43, Issue 5, pp. 1287 - 1299

Journal Article

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, ISSN 1735-8515, 10/2017, Volume 43, Issue 5, pp. 1287 - 1299

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are...

MATHEMATICS | Levy noise | Stochastic evolution equation | Ito type inequality | stochastic convolution integral | monotone operator

MATHEMATICS | Levy noise | Stochastic evolution equation | Ito type inequality | stochastic convolution integral | monotone operator

Journal Article

Random Operators and Stochastic Equations, ISSN 0926-6364, 09/2015, Volume 23, Issue 3, pp. 151 - 159

In this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itô integrals. These inequalities generalize some inequalities which...

Gronwall–Bellman inequality | Itô integral | 60H10 | 54C60 | Stochastic differential equation | Ito integral | Gronwall-Bellman inequality | Inequalities (Mathematics) | Stochastic differential equations | Analysis | Differential equations | Stochastic models | Operators | Integrals | Mathematical analysis | Uniqueness | Inequalities | Nonlinearity | Stochasticity

Gronwall–Bellman inequality | Itô integral | 60H10 | 54C60 | Stochastic differential equation | Ito integral | Gronwall-Bellman inequality | Inequalities (Mathematics) | Stochastic differential equations | Analysis | Differential equations | Stochastic models | Operators | Integrals | Mathematical analysis | Uniqueness | Inequalities | Nonlinearity | Stochasticity

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 2012, Volume 15, Issue 2, pp. 423 - 436

In this paper, we study the boundedness and stability with respect to the parameters for the mild solutions of stochastic functional evolution equations in...

Functional evolution equation | Ito-type inequality | Semimonotone | Boundedness | Demicontinuous | Mild solution | Continuity with respect to the parameters | SPACE | MATHEMATICS | demicontinuous | continuity with respect to the parameters | functional evolution equation | STABILITY | mild solution | DIFFERENTIAL-EQUATIONS | semimonotone | MONOTONE NONLINEARITY | boundedness

Functional evolution equation | Ito-type inequality | Semimonotone | Boundedness | Demicontinuous | Mild solution | Continuity with respect to the parameters | SPACE | MATHEMATICS | demicontinuous | continuity with respect to the parameters | functional evolution equation | STABILITY | mild solution | DIFFERENTIAL-EQUATIONS | semimonotone | MONOTONE NONLINEARITY | boundedness

Journal Article

8.
LARGE DEVIATIONS AND BERRY-ESSEEN INEQUALITIES FOR ESTIMATORS IN NONLINEAR NONHOMOGENEOUS DIFFUSIONS

REVSTAT-STATISTICAL JOURNAL, ISSN 1645-6726, 11/2007, Volume 5, Issue 3, pp. 249 - 267

Bounds on the large deviations probability of the maximum likelihood estimator and regular Bayes estimators, and Berry-Esseen type bound for the suitably...

maximum likelihood estimator | Berry-Esseen type inequality | Bayes estimators | nonhomogeneous diffusion processes | STATISTICS & PROBABILITY | larger deviations probability | Ito stochastic differential equation | drift parameter

maximum likelihood estimator | Berry-Esseen type inequality | Bayes estimators | nonhomogeneous diffusion processes | STATISTICS & PROBABILITY | larger deviations probability | Ito stochastic differential equation | drift parameter

Journal Article

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 3, pp. 2121 - 2167

We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in...

MARTINGALES | MATHEMATICS, APPLIED | Ito formula | exponential estimate | Burkholder-Davis-Gundy inequality | martingale type r Banach space | stochastic convolution | maximal inequality

MARTINGALES | MATHEMATICS, APPLIED | Ito formula | exponential estimate | Burkholder-Davis-Gundy inequality | martingale type r Banach space | stochastic convolution | maximal inequality

Journal Article

Mathematical Inequalities and Applications, ISSN 1331-4343, 2000, Volume 3, Issue 4, pp. 593 - 614

In this paper, we consider the exponentially asymptotic stability of the mild solutions of semilinear stochastic evolution equations of monotone type. An...

Borel-Cantelli's lemma | Sample-path stability | Itô-type inequality | Stability in the p-th moment | Stochastic evolution equations | MATHEMATICS | EXPONENTIAL STABILITY | Ito-type inequality | stochastic evolution equations | PARTIAL-DIFFERENTIAL EQUATIONS | INEQUALITY | sample-path stability | stability in the p-th moment

Borel-Cantelli's lemma | Sample-path stability | Itô-type inequality | Stability in the p-th moment | Stochastic evolution equations | MATHEMATICS | EXPONENTIAL STABILITY | Ito-type inequality | stochastic evolution equations | PARTIAL-DIFFERENTIAL EQUATIONS | INEQUALITY | sample-path stability | stability in the p-th moment

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2010, Volume 234, Issue 9, pp. 2663 - 2682

We consider extensions, developments and modifications of a result due to Halanay, and the application of “Halanay-type inequalities” in the analysis and...

Difference/differential inequalities with maxima | Deterministic & Itô delay equations | Difference/delay differential equations | Linear [formula omitted]-methods | Applications | Generalizations of Halanay’s lemma | Linear θ-methods | Generalizations of Halanay's lemma | Linear theta-methods | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | INEQUALITIES | Deterministic & Ito delay equations | THETA-METHODS | SYSTEMS | DELAY | Stability | Difference equations | Mathematical analysis | Evolutionary | Classification | Differential equations | Inequalities | Mathematical models | Time lag

Difference/differential inequalities with maxima | Deterministic & Itô delay equations | Difference/delay differential equations | Linear [formula omitted]-methods | Applications | Generalizations of Halanay’s lemma | Linear θ-methods | Generalizations of Halanay's lemma | Linear theta-methods | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | INEQUALITIES | Deterministic & Ito delay equations | THETA-METHODS | SYSTEMS | DELAY | Stability | Difference equations | Mathematical analysis | Evolutionary | Classification | Differential equations | Inequalities | Mathematical models | Time lag

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 04/2017, Volume 123, pp. 23 - 26

A concentration inequality for a specific type of the Itô integrals indexed by matrices is obtained. This type of stochastic processes appears in the framework...

Itô integral | Concentration inequality | Nonparametric function estimation | Ito integral | STATISTICS & PROBABILITY | Analysis | Gaussian processes | Equality

Itô integral | Concentration inequality | Nonparametric function estimation | Ito integral | STATISTICS & PROBABILITY | Analysis | Gaussian processes | Equality

Journal Article

Stochastics and Stochastic Reports, ISSN 1045-1129, 03/1995, Volume 53, Issue 1-2, pp. 129 - 174

A semigroup approach is used to prove existence, uniqueness and boundedness of the solution of semilinear stochastic evolution equations with monotone...

semigroup | semilinear | Ito type "energy" inequality | Stochastic evolution equations | monotone nonlinearities Burkholder type inequality | martingales

semigroup | semilinear | Ito type "energy" inequality | Stochastic evolution equations | monotone nonlinearities Burkholder type inequality | martingales

Journal Article

Stochastics and Dynamics, ISSN 0219-4937, 07/2018

Journal Article

2016 35th Chinese Control Conference (CCC), ISSN 1934-1768, 07/2016, Volume 2016-, pp. 1820 - 1825

This paper is concerned with the problem of almost sure exponential stability and moment exponential stability for a class of stochastic parabolic complex...

Neurons | Nonnegative semi-martingale convergence theorem | reaction diffusion | Stability analysis | Control theory | Delays | complex networks | strong Itô function | Biological neural networks | exponential stability | Convergence | Networks | Stability | Conferences | Neural networks | Inequalities | White noise | Diffusion

Neurons | Nonnegative semi-martingale convergence theorem | reaction diffusion | Stability analysis | Control theory | Delays | complex networks | strong Itô function | Biological neural networks | exponential stability | Convergence | Networks | Stability | Conferences | Neural networks | Inequalities | White noise | Diffusion

Conference Proceeding

Journal of Functional Analysis, ISSN 0022-1236, 10/2016, Volume 271, Issue 7, pp. 1764 - 1792

We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations...

Multiplicative gradient-type Stratonovich noise | Killing vector field | Stochastic total variation flow | Stochastic variational inequality with singular diffusivity | TOMOGRAPHY | EXISTENCE | MATHEMATICS | ITOS FORMULA | Multiplicative gradient-type | Stratonovich noise | Differential equations | Probability | Analysis of PDEs | Mathematics

Multiplicative gradient-type Stratonovich noise | Killing vector field | Stochastic total variation flow | Stochastic variational inequality with singular diffusivity | TOMOGRAPHY | EXISTENCE | MATHEMATICS | ITOS FORMULA | Multiplicative gradient-type | Stratonovich noise | Differential equations | Probability | Analysis of PDEs | Mathematics

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 01/2003, Volume 21, Issue 1, pp. 161 - 181

In this paper, we consider the exponentially asymptotic stability of the mild solutions of semilinear stochastic delay evolution equations of monotone type. An...

Borel-Cantelli's lemma | Stochastic delay evolution equations | Itoˆ inequality | Stability of the moments | Pathwise asymptotic behavior | Itô | Inequality | EXISTENCE | MATHEMATICS, APPLIED | Ito inequality | EXPONENTIAL STABILITY | stability of the moments | stochastic delay evolution equations | pathwise asymptotic behavior | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | UNIQUENESS

Borel-Cantelli's lemma | Stochastic delay evolution equations | Itoˆ inequality | Stability of the moments | Pathwise asymptotic behavior | Itô | Inequality | EXISTENCE | MATHEMATICS, APPLIED | Ito inequality | EXPONENTIAL STABILITY | stability of the moments | stochastic delay evolution equations | pathwise asymptotic behavior | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | UNIQUENESS

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 1985, Volume 20, Issue 1, pp. 1 - 40

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. Burkholder's inequalities prove to be an adequate tool to control the quadratic...

Ito-type formulas | Burkholder's inequalities | N-parameter strong martingales | N-parameter strong martingales Ito-type formulas Burkholder's inequalities

Ito-type formulas | Burkholder's inequalities | N-parameter strong martingales | N-parameter strong martingales Ito-type formulas Burkholder's inequalities

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 10/2009, Volume 27, Issue 6, pp. 1201 - 1211

In this article, we find necessary conditions for the existence of Ito Integral in a Banach space with respect to compensated Poisson random measure (cPrm)....

60G57 | 28C20 | 60G51 | Pettis and Ito integrals | Random Hilbert and Banach valued functions | Additive processes | Compensated Poisson random measures | Multiplicative noise | 46G10 | 47G99 | 46E99 | Stochastic integrals on separable Hilbert and Banach spaces | M-type 2 and type 2 Banach spaces | 60H05 | 46B09 | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | VALUES | Theorems | Integrals | Mathematical analysis | Inequalities | Hilbert space | Stochasticity | Banach space

60G57 | 28C20 | 60G51 | Pettis and Ito integrals | Random Hilbert and Banach valued functions | Additive processes | Compensated Poisson random measures | Multiplicative noise | 46G10 | 47G99 | 46E99 | Stochastic integrals on separable Hilbert and Banach spaces | M-type 2 and type 2 Banach spaces | 60H05 | 46B09 | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | VALUES | Theorems | Integrals | Mathematical analysis | Inequalities | Hilbert space | Stochasticity | Banach space

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2018, Volume 370, Issue 12, pp. 8521 - 8550

It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map...

Ito-Lyons map | p-variation | SPACES | THEOREM | INEQUALITY | STOCHASTIC CALCULUS | SIGNALS | Besov space | MATHEMATICS | Riesz-type variation | RESPECT | INTEGRATION | Besov embedding | rough path | Controlled differential equation | DIFFERENTIAL-EQUATIONS DRIVEN | FRACTAL FUNCTIONS

Ito-Lyons map | p-variation | SPACES | THEOREM | INEQUALITY | STOCHASTIC CALCULUS | SIGNALS | Besov space | MATHEMATICS | Riesz-type variation | RESPECT | INTEGRATION | Besov embedding | rough path | Controlled differential equation | DIFFERENTIAL-EQUATIONS DRIVEN | FRACTAL FUNCTIONS

Journal Article

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